In mathematics, the Hilbert symbol or norm-residue symbol is a function (–, –) from K× × K× to the group of nth roots of unity in a local field K such...

lines. Use of arrow symbols in mathematical notation is still younger and developed in the first half of the 20th century. David Hilbert in 1922 introduced...

introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol. Let p {\displaystyle p} be an...

\left({\tfrac {p}{q}}\right)=-1.} but he couldn't prove that either. Hilbert symbol (below) discusses how techniques based on the existence of solutions...

Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity...

Hilbert ring Hilbert–Poincaré series Hilbert series and Hilbert polynomial Hilbert space Hilbert spectrum Hilbert system Hilbert transform Hilbert's arithmetic...

the symbol is sometimes called a Chevalley symbol or Artin–Chevalley symbol. The local Hilbert symbol of K can be written in terms of the Artin symbol for...

a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann...

Carmichael lambda function of n). The n-th power residue symbol is related to the Hilbert symbol ( ⋅ , ⋅ ) p {\displaystyle (\cdot ,\cdot )_{\mathfrak {p}}}...

between (p/q) and (q/p). Hilbert reformulated the reciprocity laws as saying that a product over p of Hilbert norm residue symbols (a,b/p), taking values...

space Hilbert spectrum Hilbert symbol Hilbert system Hilbert transform Hilbert spectroscopy Hilbert–Huang transform Hilbert spectral analysis Hilbert-style...

Vostokov developed an important class of explicit formulas for the Hilbert symbol on local fields, which have a wide range of applications in number theory...

{4}}} , in which case we can take n = | a | {\displaystyle n=|a|} . Hilbert symbol Kronecker, L. (1885), "Zur Theorie der elliptischen Funktionen", Sitzungsberichte...

number field F, the group K2(F) is related to class field theory, the Hilbert symbol, and the solvability of quadratic equations over completions. In contrast...

"Hilbert-symbol equivalence of number fields". Tatra Mt. Math. Publ. 11: 7–16. Zbl 0978.11012. Czogała, A. (1999). "Higher degree tame Hilbert-symbol equivalence...

and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol of local class field theory. Results were mostly proved...

In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It...

see e.g. Ch. IV of. Using the local reciprocity map, one defines the Hilbert symbol and its generalizations. Finding explicit formulas for it is one of...

Hilbert's biographer Constance Reid): "Through a proof of existence, Hilbert had been able to obtain a construction"; "the proof" (i.e. the symbols on...

Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as...

mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity...

In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent...

In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation...

CITEREFRost1986 (help). The name "norm residue" originally referred to the Hilbert symbol ( a 1 , a 2 ) {\displaystyle (a_{1},a_{2})} , which takes values in...

mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible...

groups. 1897 Hilbert publishes his Zahlbericht. 1897 Hilbert rewrites the law of quadratic reciprocity as a product formula for the Hilbert symbol. 1897 Kurt...

something like a point or a line, which we still choose symbols for. By adopting this language, Hilbert thought that we could prove all theorems within any...

case of the circle, which has eccentricity e = 0. {\displaystyle e=0.} The symbol or variable for diameter, ⌀, is sometimes used in technical drawings or...

corner has been used by Peirce. Implication: the symbol → {\displaystyle \to } appeared in Hilbert in 1918;: 76  ⊃ {\displaystyle \supset } was used...

Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric...